Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 4

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If $A B = A$ and $B A = B$ , then which of the following is/are true?

50% studentsanswered this correctly

Important Questions on Matrices

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 5

If

A (θ) = [\begin{matrix} \sin θ & i \cos θ \\ i \cos θ & \sin θ \end{matrix}]

, then which of the following is not true ?

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 6

Let

A

and

B

be two non-singular matrices,

A^{T}

and

B^{T}

are the transpose matrices of

A

and

B

, respectively, then which of the following are correct?

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 7

If

B

is an idempotent matrix, and

A = I - B

, then

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 8

If

A_{1} = [\begin{matrix} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{matrix}]

and

A_{2} = [\begin{matrix} 0 & 0 & 0 & i \\ 0 & 0 & - i & 0 \\ 0 & i & 0 & 0 \\ - i & 0 & 0 & 0 \end{matrix}]

, then

A_{i} A_{k} + A_{k} A_{i}

is equal to

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 9

Suppose

a_{1}, a_{2}, a_{3}, . . .

are real numbers, with

a_{1} \neq 0 .

If

a_{1}, a_{2}, a_{3} . . . . .

are in

A . P .,

then

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 10

If

α, β and γ

are three real numbers and

A = [\begin{matrix} 1 & \cos (α - β) & \cos (α - γ) \\ \cos (β - α) & 1 & \cos (β - γ) \\ \cos (γ - α) & \cos (γ - β) & 1 \end{matrix}]

then which of following is/are true?

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 11

If

D_{1}

and

D_{2}

are two

3 \times 3

diagonal matrices, then which of the following is/are true?

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 12

Let

A

be the

2 \times 2

matrix given by

A = [a_{i j}]

where

a_{i j} \in \{0, 1, 2, 3, 4\}

such that

a_{11} + a_{12} + a_{21} + a_{22} = 4

then which of the following statement(s) is/are true?